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EE120_F'08 Outcomes List – Babak Ayazifar

COURSE LEARNING OBJECTIVES AND OUTCOMES:

This course trains students for an intermediate level of fluency with signals and systems in both

continuous time and discrete time, in preparation for more advanced subjects in digital signal processing (including audio, image and video processing), communication theory, and systemtheory, control, and robotics.

Upon successful completion, a student should:

• Be able to classify systems based on their properties: in particular, to understand ande ploit the implications of linearity, time!invariance, causality, memory, and bounded!input, bounded!out (B"B#) stability.

• $now the principles of vector spaces, including how to relate the concepts of basis,dimension, inner product, and norm to signals.

• %earn to treat signals as vectors in a vector space and ascribe geometry to that space bydefining an appropriate inner product&in both discrete!time and continuous!time, andfor both periodic and aperiodic signals.

• $now how to analy'e, design, appro imate, and manipulate signals using vector!spaceconcepts.

• etermine ourier transforms for continuous!time and discrete!time signals (or impulse!response functions), and understand how to interpret and plot ourier transformmagnitude and phase functions.

• Understand the sampling theorem and how it lin*s continuous!time signals to discrete!

time signals. "n particular, *now how to derive the sampling theorem from first principles&from the basic properties of the ourier transform+ how the spectrum of asampled signal relates to the spectrum of the original signal+ how to use the samplingtheorem to understand aliasing phenomena in the real!world (e.g., the carriage wheeleffect), and how to reduce or prevent aliasing+ and how to perform discrete!time

processing of continuous!time signals, and vice versa, using - and - converters.

• Understand the need to define two new transforms&the %aplace and transforms&totreat a class of signals broader than what the ourier transform can handle.

• Understand the combined implications of linearity and time invariance in the %aplace and transform domains. "n particular, *now how to represent the response of an %T" system

to a more general form of comple e ponential& e st

in continuous time or z n

in discrete!time&and understand that comple e ponentials are eigenfunctions of %T" systems+ usethe %aplace transform to determine the transfer function of a continuous!time %T" system+solve for a response given the input, system description and initial conditions+ and answer /uestions related to B"B# stability, including the central role of the i !a is in thetransform!domain representations of continuous!time signals and systems+ use the transform to determine the transfer function of a discrete!time %T" system+ solve for aresponse given the input, system description and initial conditions+ and answer /uestionsrelated to B"B# stability, including the central role of the unit circle in the transform!

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domain representations of discrete!time signals and systems+ represent an %T" system byits transfer function+ determine the input!output behavior of an %T" system entirely in thetransform domain, using relationships between time!domain and the fre/uency!domain(e.g., convolution in the time domain corresponds to multiplication in the fre/uencydomain)+ understand the conditions under which the transfer function of a system (or the%aplace or transform of a signal) is rational, and *now that a continuous!time %T"system with a rational transfer function can be represented by a linear, constant!coefficient differential e/uation+ and a discrete!time %T" system with a rational transferfunction can be represented by a linear, constant!coefficient difference e/uation.

• Understand the relationships among the various representations of %T" systems&linearconstant!coefficient difference or differential e/uation, fre/uency response, transferfunction, and impulse response&and infer one representation from another (e.g.,determine the impulse response from the difference e/uation, etc.).

• Understand the conditions for a time!domain function to have a ourier transform, and*now how to relate the ourier transform to its %aplace or transform.

•

Understand the various properties of the four ourier transforms, the %aplace transform,and the transform&including time!shift, modulation (fre/uency shift), duality,symmetry and anti!symmetry&and e ploit them to analy'e and design signals andsystems.

• Understand the properties, as well the analysis and design implications, ofinterconnections of %T" systems&parallel, series (cascade), and feedbac*&in the timeand transform domains.

• $now how to derive and e ploit basic concepts in communication theory, includingamplitude modulation and fre/uency modulation.

• Understand how to use the unilateral %aplace or transform to decompose the responseof an %T" system into a 'ero!state component and a 'ero!input component, and solvelinear, constant!coefficient differential or difference e/uations, with possibly non!'eroinitial conditions.

• evelop reasonably!accurate mathematical models for physical systems, find %T"appro imations to the models, produce bloc*!diagram implementations of themathematical models, and analy'e the bloc* diagram reali'ations with a view towarddesigning more comple systems or more sophisticated models.

• %earn to develop and analy'e state!space models of linear and nonlinear systems. Thisincludes drawing /ualitative plots of state trajectories+ determining internal stabilityincluding the stability of e/uilibrium points+ determining the modes of %T" systems,especially second!order systems, by performing eigenanalysis of the state transitionmatri + and developing an aptitude for modeling a multidisciplinary array of systems instate!space form.